Titlebook: Stochastic Numerics for Mathematical Physics; Grigori N. Milstein,Michael V. Tretyakov Book 2021Latest edition Springer Nature Switzerland

analogous

Numerical Methods for SDEs with Small Noise,fficient than general methods. Very often fluctuations, which affect a physical system, are small. Fortunately, as shown in this chapter, in the case of stochastic systems with small noise, it is possible to construct special high-exactness numerical methods with low time-step order and hence comput

MURKY

不透明

怪物

Random Walks for Linear Boundary Value Problems,ter . deals with mean-square approximations of SDEs in bounded domains, and its results can be applied for solving boundary value problems. However, since solutions of boundary value problems for parabolic and elliptic equations can be represented as expectations of solutions of the corresponding sy

柔美流畅

笨重

预兆好

Solving FBSDEs Using Layer Methods, FBSDEs are associated with semilinear or quasilinear PDEs. In turn, solutions of the PDEs have probabilistic representations via the FBSDEs, which are a generalization of the Feynman-Kac formula. The chapter presents numerical algorithms for solving FBSDEs in the mean-square sense. In both cases of

GORGE

Solving Parabolic SPDEs by Averaging Over Characteristics,losely related to the nonlinear filtering problem. In this chapter the method of characteristics (the generalised Feynman-Kac formula) and numerical integration of (ordinary) SDEs together with the Monte Carlo technique are exploited to propose numerical methods for linear SPDEs of parabolic type. T

Lumbar-Stenosis

水槽